Geometria “imperfetta”: Luigi Vietti, villa La Roccia a Cannobio

"The article reviews the thought and work of Luigi Vietti (leading exponent of Italian Rationalism, then author of numerous domestic architectures, especially in Sardinia and on the Alps), through the presentation of one of his most important projects: the Villa La Roccia in Cannobio on the Lago Maggiore, completed in 1936. This project is based on a previous model, the “Villa su Roccia a Sperone”, designed with a promotional target in mind. The latter was published in 1932 on «Domus Magazine » and was exposed in several Rational Architecture events. Between 1930 and 1936 he develops a new concept of architecture in relation to the site by means of topological reasoning. This article uses critical interpretation to highlight that, in Vietti’s work, his interest in emerging architecture (shown by his participation in major founding events in the period between the Two World Wars) and the link to tradition, both contextual and disciplinary, manage to coexist in an often exemplary way. In Villa La Roccia, the character of the architecture as a whole and its details are remodeled to adapt to the rocky spur of Punta d’Amore. This makes the work better merge and blend with the surroundings. Even the interiors are recalibrated in relation to the site and domestic activities, emphasizing the precious definition of details and devoting particular attention to the perceptive-emotional factors of life within it."

Semantic and Qualitative Physics-Based Reasoning on Plain-English Flow Terms for Generating Function Model Alternatives

In graph-based function models, the function verbs and flow nouns are usually chosen from predefined vocabularies. The vocabulary class definitions, combined with function modeling grammars defined at various levels of formalism, enable function-based reasoning. However, the text written in plain English for the names of the functions and flows is presently not exploited for formal reasoning. This paper presents a formalism (representation and reasoning) to support semantic and physics-based reasoning on the information hidden in the plain-English flow terms, especially for automatically decomposing black box function models, and to generate multiple design alternatives. First, semantic reasoning infers the changes of flow types, flow attributes, and the direction of those changes between the input and output flows attached to the black box. Then, a representation of qualitative physics is used to determine the material and energy exchanges between the flows and the function features needed to achieve them. Finally, a topological reasoning is used to infer multiple options of composing those function features into topologies and to thus generate multiple alternative decompositions of the functional black box. The data representation formalizes flow phases, flow attributes, qualitative value scales for the attributes, and qualitative physics laws. An eight-step algorithm manipulates these data for reasoning. This paper shows four validation case studies to demonstrate the workings of this formalism.

Separated Flow Topology in Compressors

When a multistage high-speed compressor is operated away from its design point, extreme incidence is caused in some blade rows. This results in large, localized separations that are three dimensional in nature. In this paper, topological reasoning is used to describe the behavior of these three-dimensional separations. It is shown that two classes of separation exist: one in which the flow progresses from attached to separate in a smooth way and another where there is a discontinuity in the response of the flow topology. It is shown that the global structure of the flow depends on the type of topological response that occurs. When the response is discontinuous, nonaxisymmetric cells of separated blades are formed. When the response is smooth, the resultant separated flow is axisymmetric. The paper is split into two broad sections: The first section presents examples of the two different classes of topological response that can occur in a single blade row, and it also shows how an engineer can achieve a different response by altering the blade design. The second section covers the analysis of a multistage high-speed compressor. The compressor initially presents the discontinuous behavior with rotating cells of separations. It is then redesigned to reduce the severity of the cell behavior or remove it entirely.

Multi-agent path topology in support of socially competent navigation planning

We present a navigation planning framework for dynamic, multi-agent environments, where no explicit communication takes place among agents. Inspired by the collaborative nature of human navigation, our approach encodes the concept of coordination into an agent’s decision making through an inference mechanism about collaborative strategies of collision avoidance. Each such strategy represents a distinct avoidance protocol, prescribing a distinct class of navigation behaviors to agents. We model such classes as equivalence classes of multi-agent path topology, using the formalism of topological braids. This formalism may naturally encode any arbitrarily complex, spatiotemporal, multi-agent behavior, in any environment with any number of agents into a compact representation of dual algebraic and geometric nature. This enables us to construct a probabilistic inference mechanism that predicts the collective strategy of avoidance among multiple agents, based on observation of agents’ past behaviors. We incorporate this mechanism into an online planner that enables an agent to understand a multi-agent scene and determine an action that not only contributes progress towards its destination, but also reduction of the uncertainty of other agents regarding the agent’s role in the emerging strategy of avoidance. This is achieved by picking actions that compromise between energy efficiency and compliance with everyone’s inferred avoidance intentions. We evaluate our approach by comparing against a greedy baseline that only maximizes individual efficiency. Simulation results of statistical significance demonstrate that our planner results in a faster uncertainty decrease that facilitates the decision-making process of co-present agents. The algorithm’s performance highlights the importance of topological reasoning in decentralized, multi-agent planning and appears promising for real-world applications in crowded human environments.

Relations Between Spatial Calculi About Directions and Orientations (Extended Abstract)

A qualitative representation of space and/or time provides mechanisms which characterize the essential properties of objects or configurations. The advantages over quantitative representations can be: (1) a better match with human concepts related to natural language, and (2) better efficiency for reasoning. The two main trends in qualitative spatial constraint reasoning are topological reasoning about regions and reasoning about directions between points and straight lines and orientations of straight lines or configurations derived from points. In this work, we apply universal algebraic tools to binary qualitative calculi and their relations.